Abstract: A numerical algorithm, based on initial value problem, using local parameterisation continuation technique is proposed in this paper for the bifurcation analysis of a sample power system model with Load Tap Changer (LTC). Bifurcation diagrams of steady state solutions are constructed by the application of the proposed algorithm. From the bifurcation diagrams, the existence of various bifurcation points such as Unstable Hopf Bifurcation (UHB), Stable Hopf Bifurcation (SHB), Cyclic Fold Bifurcation (CFB), Saddle Node Bifurcation (SNB) and Period Doubling Bifurcation (PDB) are identified with the use of tools of nonlinear dynamics. The role of LTC on the occurrence of Hopf bifurcation, SNB, incidence of dynamic and static voltage collapse and in augmenting the loadability limit of a sample power system is analysed. It is shown that LTC can only be temporarily relied upon to stop or delay the dynamic instability mechanism.